The most fundamental way to define a culture is through its art. Geography, food, religion, technology and government are critical as well, of course, but none of those quite get to the soul of a people in the same way. With fantasy fiction, we're mostly dealing with forms of art of limited technology: painting, sculpture, architecture, music, poetry, literature and theater.
Music tends to be the way many fantasy writers go, to the point of cliché. Especially with songs. This is probably one of the quirks of genre that we inherited from Tolkien. Let's face it, Tolkien loved his songs. Personally, when I was reading him, whenever I saw indented, italicized text, I knew it was time to skip ahead a bit. The same thing with poetry. Now, part of the reason why these parts of a book seem so disposable is because the writers are not the poets/songsmiths of the ages that the work purports them to be. It's one thing to say that a poem is a soulcrushing work of rhyme and meter that drives men to tears; it's another to actually write it. I could do without it, personally. I could also do without mention of lutes or mandolins.*
Painting, sculpture and architecture, I'll admit, are a little out of my ken. Especially architecture. For painting and sculpture, I tend to go in the direction of what they depict, rather than how they're depicted. That's a nice way to drop a little worldbuilding history into the mix without it being as much of an infodump. At the very least, having your characters seeing a painting or statue of a former king gives a slightly more organic way to drop in some background.
Literature and theater are my favorite, though I tend to again go for what such pieces are about (and what that says about the culture) over trying to come up with excerpts. In Thorn of Dentonhill, I have a snippet of dialogue from Three Men and Two Wives, which is going on in the background while Veranix is searching for someone in the public square. Three Men and Two Wives is one of the ribald comedies of Darren Whit, a playwright from the previous century that I occasionally mention that is the Druth equivalent of Shakespeare**. At a different point, I have Kaiana quoting from one of Whit's history plays, Queen Mara. But, again, only snippets. And in Holver Alley Crew, there's mention of the banned play The Marriage of the Jester, which is being performed in an especially shabby part of town. While Three Men and Two Wives is a lusty, romantic farce (filled with crossdressing and confused identity), The Marriage of the Jester is little more than smut, presented to give the audience a cheap thrill, or for a little more coin, the opportunity to join in.
I have to admit, I have fun just brainstorming potential play titles.
I intend to include a little bit of loftier theatre in Way of the Shield-- perhaps even an opera, if I can make it work. Amanda Downum's The Bone Palace has a nice bit where her main characters go to the opera, and it's the blood-soaked tragedy kind.
The other element I'm interested in adding to the mix is the use of magic in creating art. I've hinted around that in Way of the Shield as well. Still pondering that. It's something I'd like to do, but at the same time, I don't want to stop the story dead in its tracks just to include it.
*- Yes, historical, but they also come off as Fantasy Clichés.
**- I also have some equivalents to Jonson, Marlowe and Webster. Definitely Webster. The Druth do so love a blood-soaked tragedy. Especially since Whit was rarely a tragedist.